A) \[(\pi \mu Bb)a\]
B) \[(2\pi \mu Bb)\Delta a\]
C) \[(\pi \mu Bb)\Delta a\]
D) \[(4\pi \mu Bb)\Delta a\]
Correct Answer: D
Solution :
[d]: Bulk modulus, \[\text{B}=\frac{\text{Normal}\,\text{stress}}{\text{Volumetric}\,\text{strain}}\] \[P=\frac{N}{A}=\frac{N}{(2\pi a)b}\] Volumetric strain \[=\frac{2\pi a\Delta a\times b}{\pi {{a}^{2}}b}=\frac{2\Delta a}{a}\] \[\therefore \]\[B=\frac{N}{2\pi ab}\times \frac{a}{2\Delta a}\]\[N=4\pi b\Delta a\times B\] \[\therefore \]Required force = Frictional force \[=\mu N=(4\pi \mu Bb)\Delta a\]You need to login to perform this action.
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